Late to the party here, but will chime in if others find this thread via search.

I have only gone over the "pass" SE of the tarn below Silliman. The USGS quad shows a permanent snowfield just to its west.

From the west, follow a gully/chute straight for the pass. Near the top, you will probably have to come out of the chute and scramble up some clean slabs. A straightforward Class 2+.

The east side is messier. If your longer term goal is to stay along the crest, you want to lose as little elevation as possible. But contouring across the talus and slabs on the east side of the pass is not very fun, or efficient. Instead, it's probably best to descend to about 10,400 feet, contouring where possible along the way. Wrap around the forested ridge (above the "I" in NATIONAL) and drop to the head of the wetlands.

From the wetlands, it's straightforward again. Ascend to the tarns at 10410. Good travel the whole way up.